XXX - Not complete yet!!!
Name

    SGIX_nurbs_eval

Name Strings

    GL_SGIX_nurbs_eval

Version

    $Date: 1998/02/12 18:24:45 $ $Revision: 1.6 $

Number

    XXX

Dependencies

    None

Overview

    This extension adds a new evaluators type, NURBS.  NURBS are a compact
    representation of the datasets that many CAD and entertainment industry
    customers are already using.  The creation of a new interface allows for
    levels of performance not achievable with the current evaluators API.

    The current evaluators interface supports only Bezier curves, which suffer
    from several disadvantages:  Beziers are a wasteful of memory and graphics
    interface bandwidth; Beziers representations are often larger than
    the representations of the tesselated surfaces they are used to render;
    Beziers are not a native format used by CAD and entertainment applications.

    In the new NURBS extension, every effort has been made to extend the
    existing evaluators interface, rather than define a completely new set of
    interfaces and state. 

Issues

    * Should it be NURB or NURBS?
    
    I'm choosing NURBS since it matches the GLU spec and glu extensions.
    This does not agree with Farin's usage in the literature, but does agree
    with many other authors.

New Procedures and Functions

    void NurbsKnots1SGIX[fd]( enum target,
			      int uknotcount, T *uknots );
    void NurbsKnots2SGIX[fd]( enum target,
			      int uknotcount, int vknotcount,
			      T *uknots, T *vknots );

New Tokens

    Accepted by the <cap> parameter of Enable, Disable, and IsEnabled, and
    by the <pname> parameter of GetBooleanv, GetIntegerv, GetFloatv, and
    GetDoublev:

	MAP1_VERTEX_3_NURBS_SGIX	0x81CB
	MAP1_VERTEX_4_NURBS_SGIX	0x81CC
	MAP1_INDEX_NURBS_SGIX		0x81CD
	MAP1_COLOR_4_NURBS_SGIX		0x81CE
	MAP1_NORMAL_NURBS_SGIX		0x81CF
	MAP1_TEXTURE_COORD_1_NURBS_SGIX	0x81E0
	MAP1_TEXTURE_COORD_2_NURBS_SGIX	0x81E1
	MAP1_TEXTURE_COORD_3_NURBS_SGIX	0x81E2
	MAP1_TEXTURE_COORD_4_NURBS_SGIX	0x81E3
	MAP2_VERTEX_3_NURBS_SGIX	0x81E4
	MAP2_VERTEX_4_NURBS_SGIX	0x81E5
	MAP2_INDEX_NURBS_SGIX		0x81E6
	MAP2_COLOR_4_NURBS_SGIX		0x81E7
	MAP2_NORMAL_NURBS_SGIX		0x81E8
	MAP2_TEXTURE_COORD_1_NURBS_SGIX	0x81E9
	MAP2_TEXTURE_COORD_2_NURBS_SGIX	0x81EA
	MAP2_TEXTURE_COORD_3_NURBS_SGIX	0x81EB
	MAP2_TEXTURE_COORD_4_NURBS_SGIX	0x81EC

    Accepted by the <value> parameter of GetMap[ifd]v:

	NURBS_KNOT_COUNT_SGIX		0x81ED
	NURBS_KNOT_VECTOR_SGIX		0x81EE

Additions to Chapter 2 of the 1.0 Specification (OpenGL Operation)

    None

Additions to Chapter 3 of the 1.0 Specification (Rasterization)

    None

Additions to Chapter 4 of the 1.0 Specification (Per-Fragment Operations
and the Frame Buffer)

    None

Additions to Chapter 5 of the 1.0 Specification (Special Functions)

    Evaluators are extended to support both the existing specification, which
    is a Bezier formulation, and a new NURBS formulation.  New enable tokens
    are used to enable NURBS evaluation when it is desired.

  Basis Functions:

    NURBS polynomials for curves are defined as follows:
    Consider the R^k-valued polynomial q(u) is defined by 
	 q(u) = sum(i=0,n) N_i^d(u) * R_i
    with N_i^d(u) =    N_i^(d-1)(u) * (u-u(i-1))/(u(i+d-1)-u(i-1)) +
		    N(i+1)^(d-1)(u) * (u(i+d)-u)/(u(i+d)-u_i)
    the i_th NURBS basis polynomial of degree d.

    Each R_i is a control point, and each u_i is a knot-value.
    The complete set of {u_i} values is called the knot vector. 

  Map1[fd]:

    When NURBS evaluation is enabled, the <order> parameter to the Map1[fd]
    function is not really the mathematical order of the NURBS polynomial.
    Instead, the <order> parameter merely determines the size of the array
    given as input to Map1[fd] or Map2[fd].  In other words, the <order>
    parameter only determines the size of the valid GL state for the map
    array; it does not really capture the mathematical order of the curve or
    surface. 

    Note that it is still true that the <order> parameter to Map1[fd] is equal
    to n+1 in the equation defining NURBS polynomials at the beginning of this
    section. 

  Map2[fd]:

    NURBS polynomials for surfaces are defined as bivariate polynomials using
    the same N_i^d basis functions as NURBS curves:
	q(u,v) = sum(i=0,n) sum(j=0,m) N_i^d(u) * N_j^c(v) * R_ij

  NurbsKnots1SGIX:
  NurbsKnots2SGIX:

    The <target> parameter must be one of GL_MAP1_VERTEX_3, GL_MAP1_VERTEX_4,
    GL_MAP1_COLOR_4, GL_MAP1_INDEX, GL_MAP1_NORMAL, GL_MAP1_TEXTURE_COORD_1,
    GL_MAP1_TEXTURE_COORD_2, GL_MAP1_TEXTURE_COORD_3, GL_MAP1_TEXTURE_COORD_4,
    GL_MAP2_VERTEX_3, GL_MAP2_VERTEX_4, GL_MAP2_COLOR_4, GL_MAP2_INDEX,
    GL_MAP2_NORMAL, GL_MAP2_TEXTURE_COORD_1, GL_MAP2_TEXTURE_COORD_2,
    GL_MAP2_TEXTURE_COORD_3, or GL_MAP2_TEXTURE_COORD_4.

    The knots vectors are defined by the new functions NurbsKnots1SGIX and
    NurbsKnots2SGIX.  The size of the knot vectors, <uknotcount> and
    <vknotcount> implicitly define the degree of the NURBS curves or surfaces
    defined.  For curves, the degree is defined as:
	d = <uknotcount> - <uorder> + 1
    For surfaces, the second degree is defined as:
	c = <vknotcount> - <vorder> + 1

    The entries from the <uknots> and <vknots> input arrays are immediately
    copied by the GL by the completion of this procedure.

  EvalCoord[12][fd]:
  EvalCoord[12][fd]v:
  EvalPoint[12]:
  EvalMesh[12]:

    For all of the new MAP1_XXX_NURBS tokens, when MAP1_XXX_NURBS is disabled,
    the evaluation functions, EvalCoord1[fd], EvalCoord1[fd]v, EvalPoint1, and
    EvalMesh1 all evaluate Bezier curves for the given map as usual.  When
    MAP1_XXX_NURBS is enabled, the evaluation functions instead evaluate NURBS
    curves.  Similarly, the new MAP2_XXX_NURBS tokens are used to enable NURBS
    surface evaluation for the functions EvalCoord2[fd], EvalCoord2[fd]v,
    EvalPoint2, and EvalMesh2.   

Additions to Chapter 6 of the 1.0 Specification (State and State Requests)

    None

Additions to the GLX Specification

    None

GLX Protocol

    XXX - Not figured out yet.

Dependencies on other extensions

    None

Errors

    INVALID_VALUE is generated if NurbsKnots[12]SGIX parameter <uknotcount> or
    <vknotcount> are negative or greater that or equal to MAX_EVAL_ORDER.

    INVALID_VALUE is generated if <uorder> > <uknotcount>+1 when any of 
    EvalCoord1[fd], EvalCoord1[fd]v, EvalPoint1, or EvalMesh1 are called if
    both of MAP1_XXX and MAP1_XXX_NURBS_SGIX are enabled.

    INVALID_VALUE is generated if <uorder> > <uknotcount>+1 or <vorder> >
    <vknotcount>+1 when any of EvalCoord2[fd], EvalCoord2[fd]v, EvalPoint2, or
    EvalMesh2 are called if both of MAP2_XXX and MAP2_XXX_NURBS_SGIX are
    enabled.

New State

									Initial
    Get Value				Get Command	Type	Value	Attrib
    ---------				-----------	----	-------	------
    MAP1_VERTEX_3_NURBS_SGIX		glIsEnabled	B	FALSE	eval/enable
    MAP1_VERTEX_4_NURBS_SGIX		glIsEnabled	B	FALSE	eval/enable
    MAP1_INDEX_NURBS_SGIX		glIsEnabled	B	FALSE	eval/enable
    MAP1_COLOR_4_NURBS_SGIX		glIsEnabled	B	FALSE	eval/enable
    MAP1_NORMAL_NURBS_SGIX		glIsEnabled	B	FALSE	eval/enable
    MAP1_TEXTURE_COORD_1_NURBS_SGIX	glIsEnabled	B	FALSE	eval/enable
    MAP1_TEXTURE_COORD_2_NURBS_SGIX	glIsEnabled	B	FALSE	eval/enable
    MAP1_TEXTURE_COORD_3_NURBS_SGIX	glIsEnabled	B	FALSE	eval/enable
    MAP1_TEXTURE_COORD_4_NURBS_SGIX	glIsEnabled	B	FALSE	eval/enable
    MAP2_VERTEX_3_NURBS_SGIX		glIsEnabled	B	FALSE	eval/enable
    MAP2_VERTEX_4_NURBS_SGIX		glIsEnabled	B	FALSE	eval/enable
    MAP2_INDEX_NURBS_SGIX		glIsEnabled	B	FALSE	eval/enable
    MAP2_COLOR_4_NURBS_SGIX		glIsEnabled	B	FALSE	eval/enable
    MAP2_NORMAL_NURBS_SGIX		glIsEnabled	B	FALSE	eval/enable
    MAP2_TEXTURE_COORD_1_NURBS_SGIX	glIsEnabled	B	FALSE	eval/enable
    MAP2_TEXTURE_COORD_2_NURBS_SGIX	glIsEnabled	B	FALSE	eval/enable
    MAP2_TEXTURE_COORD_3_NURBS_SGIX	glIsEnabled	B	FALSE	eval/enable
    MAP2_TEXTURE_COORD_4_NURBS_SGIX	glIsEnabled	B	FALSE   eval/enable

    NURBS_KNOT_COUNT_SGIX		GetMapiv	9XZ+	 0	
    NURBS_KNOT_COUNT_SGIX		GetMapiv	9X2XZ+	 0,0	
    NURBS_KNOT_VECTOR_SGIX		GetMapdv	9X7*XR	 undef.	
    NURBS_KNOT_VECTOR_SGIX		GetMapdv	9X2X7*XR undef.	


New Implementation Dependent State

    None